a load of 2kg produces an extension of 1mm in a wire of 3m in length and 1mm in diameter. The young's modulus of wire will be? answer is 7.48×10^10 Nm-2
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The young's modulus of the wire is 7.48 x 10¹⁰ Nm⁻²
Explanation :
The applied load =F = mg = 2 x 9.8 = 19.6 N
diameter = 1 mm = 1 x 10⁻³ m
=> radius = 0.5 x 10⁻³ m
Area , A = 3.14r² = 3.14 x 0.25 x 10⁻⁶
= 0.785 x 10⁻⁶
We know that
stress = FORCE/AREA
= 19.6/(0.785 x 10⁻⁶)
= 24.96 x 10⁶
change in length, ΔL = 1 mm = 10⁻³ m
Length, L = 3 m
hence strain = ΔL/L
= 10⁻³/3
we know that young's modulus is given by the ratio of stress and strain,
Hence
E = 24.96 x 10⁶/10⁻³/3
= 74.8 x 10⁹
= 7.48 x 10¹⁰ Nm⁻²
Hence the young's modulus of the wire is 7.48 x 10¹⁰ Nm⁻²
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